Method of operating a nuclear magnetic resonance spectrometer

ABSTRACT

In a method of operating a nuclear magnetic resonance (NMR) spectrometer in relation to a sample comprising two types of nuclei, a sequence of radiofrequency pulses and delay periods is applied using two different radiofrequency coils, one for each type of nucleus, each coil providing an inhomogeneous radiofrequency field, so that the two coils generate separate but overlapping sensitive volumes for each of the two types of nuclear species, whereby signal intensity is substantially limited to the overlap volume.

The invention relates to a method of operating a nuclear magneticresonance spectrometer in relation to a sample comprising two types ofnuclei, in which a sequence of radiofrequency pulses and delay periods,the pulses thereof having two different radiofrequencies correspondingto the two types of nuclei, is applied to the two nuclei such that thenuclear scalar coupling interactions between the two types of nuclei areallowed to evolve.

Such a method is disclosed in No. EP-A-0 089 034, and consists inapplying special pulse sequences, called DEPT sequences, to relativelyhomogeneous rf coils positioned adjacent to the sample, which isincluded in a sample vessel. The result of this method are NMR spectraproviding information about the chemical environment of the two nuclearspins and thus information about the structure of the chemical compoundsin which the two nuclear spins are found.

Further, in Journal of Magnetic Resonance 53, 365 (1982) and 54, 149(1983), in Chemical Physics Letters 99, 310 (1983) and in Bull. Magn.Reson. 5, 191 (1983), a method of operating a nuclear magnetic resonancespectrometer is described in which an rf coil is used to generate an rfmagnetic field when an rf pulse is applied thereto, said rf magneticfield varying grossly and continuously throughout the sample volume. Asgenerally known in NMR-spectroscopy, an rf pulse of particular lengthand power rotates the magnetization of a nuclear species through anangle θ, so that at any point in the sample space this angle isproportional to the strength of the rf field at that point in space.According to the said references, phase-cycled pulse sequences known as"depth pulse schemes or sequences" or just "depth pulses" are used toacquire NMR signals from sample regions where the θ pulse angle isbetween particular predetermined limits. These limits define a"sensitive volume" in sample space. This known method has been confinedto a single nuclear species.

It is the object of the invention to provide a method to acquire NMRsignals from defined regions or "localized volumes" in an extendedsample giving information about the structure of chemical compoundsincluded in this sensitive volume.

This object is achieved by applying the pulses of different radiofrequencies to two different coils, respectively, each of which providesan inhomogeneous radiofrequency field, the two coils generating separatebut overlapping sensitive volumes for each different nuclear species, sothat a significant signal intensity will only be obtained from sampleregions where the two sensitive volumes overlap.

Included within the scope of this invention is the application of anyheteronuclear pulse sequence with two separate heteronuclearinhomogeneous rf coils defining different sensitive volumes, such thatsignal intensity is only obtained from one well defined localized volumein a larger sample, in which region the sensitive volumes overlap. Apreferred heteronuclear pulse sequence is the DEPT pulse sequence asdisclosed in No. EP-A-0 089 034. However, also heteronuclear spin-echosequences and selective polarization transfer sequences may be used togenerate two overlapping sensitive volumes.

Inhomogeneous rf coils of any shape are included within the scope ofthis invention and it is clearly possible to vary the shape and theposition of the coils to tailor the shape of the final localized region,as defined by the two overlapping sensitive volumes.

The invention, its objectives and features will be better understood andappreciated from the following detailed description of the theoryunderlying the invention and of specific examples of use of theinventive method, with reference to the accompanying drawings. Themethods are exemplified in terms of ¹³ CH_(n) systems (n=1,2,3), a mostimportant problem in in vivo spectroscopy which could benefit from theinvention. The terminology used before and in the following descriptionis commonly used in the NMR literature.

In the drawings:

FIG. 1 is a diagram showing the dependence of signal intensity on the ¹³C θ pulse length using the pulse sequence (π/2)[H,x]-(2J)⁻¹ -π[H];2θ[±x]; θ; 2θ[±x,±y]-(2J)⁻¹ -(π/4)[H,y]; 2θ[±x,±y]-(2J)⁻¹ -acquire ¹³ Csignal.

FIG. 2 is a diagram showing the dependence of signal intensity on the ¹H φ pulse length using the pulse sequence 2φ[±x]; φ[x]-(2J)⁻¹-2φ[±x,±y]; (π/2)[C]-(2J)⁻¹ -(φ/2)[y]; π[C]-(2J)⁻¹ -acquire ¹³ C signal.

FIG. 3 is a schematic representation of cross section through the coilsand the sample.

FIG. 4 is a diagram showing the dependence of signal intensity on the ¹³C φ pulse length using a ¹ H spin-echo sequence and particular simpleand composite ¹³ C pulses specified in the description.

As mentioned above, a well-established pulse sequence for polarizationtransfer between spin-half systems is the DEPT sequence. Forpolarization transfer from ¹ H to ¹³ C it may be written ##EQU1## J isthe ¹³ C-¹ H coupling constant for directly-bonded nuclei. The π/4[±y]pulse takes a compromise angle to simultaneously yield polarizationtransfer for methyl (CH₃), methylene (CH₂) and methine (CH) groups, thepolarization transfer enhancement being near maximum for CH₃ and CH₂groups and 71% of maximum for CH groups. The [±y] alternation of thephase of this pulse is generally employed in conjunction withalternation of receiver phase to eliminate the natural ¹³ Cmagnetization. The DEPT sequence is a good pulse sequence to investigatefor application to coils which produce inhomogeneous rf fields, becauseit contains the smallest possible number of pulses for polarizationtransfer across a range of chemical shifts: three pulses to achieve thetransfer and two refocusing (π) pulses to refocus the ¹ H and ¹³ Cchemical shift.

For inhomogeneous rf coils, the pulse angles will vary continuouslythroughout the sample, and it is more representative to write the ¹³ Cpulses as θ and 2θ, respectively, and the ¹ H pulses as φ, 2φ, and φ/2,respectively. In sample regions where the pulse angles diverge greatlyfrom the ideal π/4, π/2, and π angles, polarization transfer will occurwith much lower efficiency. As the 2φ pulses diverge from π, thechemical shift of the ¹ H spins is refocused with less efficiency and sopolarization transfer will also depend on the magnitude of the ¹ Hshift. Other complications will arise. For example, depending on the ¹ Hshift, when the 2φ pulse is close to π/2, polarization transfer willalso occur via the first three pulses in an INEPT-like mechanism (seeMorris and Freeman, J. Am. Chem. Soc., 101, 760 (1979). As the 2θ pulsesdiverge from π, the chemical shift of the ¹³ C spins is refocused withless efficiency, and phase errors occur in the final signal.

The variable effect of variable chemical shift, when 2θ and 2φ divergefrom π, can be entirely removed by cycling the phase of these pulsesthrough all four quadrants, written 2θ[±x,±y] for example, during aseries of transients. The basic DEPT sequence for inhomogeneous rf coilsthus becomes ##EQU2##

The phase cycling of the ¹³ C pulse is easily explained in terms of theabove-mentioned Bendall-references. The θ-(2J)⁻¹ -2θ-(2J)⁻¹ - portion ofDEPT can be thought of as a spin-echo sequence whose purpose is torefocus the ¹³ C shift. Thus, cycling the phase of the 2θ pulse makesthe final signal magnitude independent of the ¹³ C chemical shift. Thephase cycling of the 2θ pulse can be explained in the same way if theφ-(2J)⁻¹ -2φ-(2J)⁻¹ - portion of the DEPT sequence is also considered tobe a spin-echo sequence. Although these simple analogies are helpful, itis preferable to establish these phase-cycled pulses, and others used indepth pulse schemes, by rigorous theory.

With phase cycling of both the 2θ and 2φ pulses, a cycle of 16transients is necessary. In the manner previously described for depthpulses, the receiver phase must be inverted whenever either of thephases of the 2θ or 2φ pulses are changed from ±x to ±y. The phasecycling of the 2φ pulse has no effect on the natural ¹³ C magnetization,and so inversion of the receiver phase when the 2φ pulse phase ischanged from ±x to ±y eliminates this natural magnetization.Consequently, alternation of the φ/2 pulse phase (written π/4[±y] forideal pulses) is not required when the 2φ[±x,±y] phase cycle is used.

In the following work we represent the action of a φ[±x] additive pulsecycle on an angular momentum operator I by an operator T(I_(x),φ), forwhich we can deduce the relations for the average effect per transient,by explicitly adding the results for φ[+x] and φ[-x], and dividing bythe number of transients:

    T(I.sub.x, φ)I.sub.z T.sup.+ (I.sub.x,φ)=I.sub.z cos φ[1]

    T(I.sub.x,φ)I.sub.x T.sup.+ (I.sub.x,φ)=I.sub.x    [ 2]

    T(I.sub.x,φ)I.sub.y T.sup.+ (I.sub.x,φ)=I.sub.y cos φ[3]

with results for T(I_(y),φ) obtained by cyclic permutations of x,y,z.Similarly the four-phase operator F(I,φ) describing the action ofφ[±x,±y] with receiver addition for ±x and subtraction for ±y can beshown to have the properties, where again we have normalized by dividingby the number of transients (four):

    F(I,φ)I.sub.z F.sup.+ (I,φ)=0                      [4]

    F(I,φ)I.sub.x F.sup.+ (I,φ)=I.sub.x sin.sup.2 (φ/2)[5]

    F(I,φ)I.sub.y F.sup.+ (I,φ)=-I.sub.y sin.sup.2 (φ/2)[6]

and so

    F(I,φ)I.sup.+ F.sup.+ (I,φ)=I.sup.- sin.sup.2 (φ/2)[7]

We consider the DEPT sequence in the form ##EQU3## and follow theHeisenberg picture approach (Pegg and Bendall, Journal of MagneticResonance 53, 229 (1983)) to find the signal which is given by the realand imaginary parts of <I⁺ (t)> where ##EQU4## where we have substitutedthe projection operator form of I⁺ for a spin-half nucleus. Theexpression for U is found as described in the cited reference, exceptthat now we also include the two-phase and four-phase operators T and Fdescribed above. The action of the four-phase pulse is two-fold: itrefocuses in the same way as a perfect π[x] pulse, and it reduces themagnitudes of the transverse vector components by a factor sin² (φ/2),in accord with [4], [5] and [6]. The refocusing property when acting onthe transverse components can be seen by comparing [5] and [6] with theaction of a perfect π[x] pulse. Consequently we can ignore chemicalshift effects in the following.

Substituting for a part of U to calculate the effect of the θ₃ [±x,±y]pulse in DEPT sequence [C]: ##EQU5## from [7]. We note that this is justsin² (θ₃ /2) multiplied by the normal DEPT result at this stage.

Continuing, that is inserting the next factors in U, which involve thepulses θ₁ [±x]; θ₂ [x], and for convenience omitting the factor sin² (θ₃/2) for now, we have

    I.sup.+ (+)α . . . T(I.sub.x,θ.sub.1) exp (iI.sub.x θ.sub.2)I.sup.-  exp (-iI.sub.x θ.sub.2)T.sup.+ (I.sub.x,θ.sub.1)P(S) . . .                         [10]

where P(S) includes all the factors involving S in [9]. As for the basicDEPT sequence, only the term involving an I_(z) component which resultsfrom [10] will give a non-zero contribution to the polarization transfersignal. This term is proportional to

    sin θ.sub.2 T(I.sub.x,θ.sub.1)I.sub.z T.sup.+ (I.sub.x,θ.sub.1)=sin θ.sub.2 cos θ.sub.1 I.sub.z[ 11]

which follows from [1].

Thus θ₁ [±x] and θ₂ [x] introduce extra factors cos θ₁ and sin θ₂respectively into the overall signal. Thus, ignoring these factors fornow and continuing by inserting the next factor into U, which involvesthe pulse cycle φ₂ [±x,±y] we find that the signal is proportional to

    . . . F(S,φ.sub.2)P(S)F.sup.+ (S,φ.sub.2) . . . = . . . F(S,φ.sub.2) exp (-iS.sub.y 2φ.sub.3) exp (iS.sub.z 2π)F.sup.+ (S,φ.sub.2) . . .

where we have used standard commutation relations to simplify P(S) asshown. Now for a group ¹³ CH_(n) the value of exp (iS_(z) 2π) is just(-1)^(n), so we have to find F(S),φ₂) exp (-iS_(y) 2φ₃)F⁺ (S,φ₂).Because F is not unitary, this evaluation requires some care. We seethat the result of the F operator is equivalent to the signal producedby T(S_(x),φ₂) minus that produced by T(S_(y),φ₂) so we need to evaluate

    -exp (-iS.sub.y 2φ.sub.3)+T(S.sub.x,φ.sub.2) exp (-iS.sub.y 2φ.sub.3)T.sup.+ (S.sub.x,φ.sub.2)                [12]

and divide this by two to find the average effect per transient. Thesecond term is one-half of ##EQU6## where S_(x) ^(i) is the operator forthe i-th proton in the group ¹³ CH_(n), and the second term in theexpression is obtained from the first by replacing φ₂ by -φ₂. The firstterm becomes ##EQU7## In finding this product we can neglect terms suchas S_(y) ^(i) S_(y) ^(i), which are of order higher than one, becausethe expectation values arising from such terms will involve powersgreater than one of the small constant K in the high temperatureBoltzmann distribution, and are therefore negligible. Including the term(φ₂ →-φ₂) this leaves us, after division by two, with

    cos.sup.n φ.sub.3 -2i cos.sup.n-1 φ.sub.3 sin φ.sub.3 S.sub.y cos φ.sub.2                                           [ 14]

The first term in [12] is ##EQU8## and, using the same arguments asabove in its evaluation, we obtain

    -cos.sup.n φ.sub.3 -2i cos.sup.n-1 φ.sub.3 sin φ.sub.3 S.sub.y,[16]

so adding [14] and [16] and dividing by two gives us a resultproportional to

    cos.sup.n-1 φ.sub.3 sin φ.sub.3 S.sub.y (1-cos φ.sub.2)/2,

which is just a factor sin² (φ₂ /2) times the normal DEPT result.Continuing with the evaluation of the signal, we no look at, againignoring the multiplication factors found so far, ##EQU9## The finalstep is to include φ₁ [±y], giving a signal

    <I.sup.+ (t)>α<T(S.sub.y,φ.sub.1)S.sub.x T.sup.+ (S.sub.y φ.sub.1)>cos φ+<T(S.sub.y,φ.sub.1)S.sub.z T.sup.+ (S.sub.y,φ.sub.1)>sin φ

From the cyclic permutations of [1], [2] and [3] we see that the firstterm is proportional to <S_(x) > which is zero. The second term gives asignal proportional to cos φ₁ sin φ. Gathering all the constants we seethat the signal is

    cos φ.sub.1 sin φ sin.sup.2 (φ.sub.2 /2) cos θ.sub.1 sin θ.sub.2 sin.sup.2 (θ.sub.3 /2)f(φ.sub.3)  [17]

where f(φ₃) is the normal DEPT signal.

The cycled pulses may be used more than once, for example in place of φ₁[±y] we might use φ₁ [±y]φ₄ [±y]. The effect of such repetition can befound by modifying the above derivation at the appropriate point. Wefind easily that φ₄ [±y] just introduces another factor cos φ₄ and soon. Addition of θ₄ [±x] before θ₁ [±x] introduces a factor cos θ₄. Wecan even use multiple refocusing cycles, introducing an extraappropriate multiplicative factor for each cycle. Providing there are anodd number of cycles at each refocusing point, refocusing will bemaintained.

From equation [17], sequence [B] yields signal intensity proportional to

    θ sin.sup.3 θ sin.sup.3 φf(φ/2)        [18]

where f(φ/2) is sin (φ/2), sin φ and 0,75[sin (φ/2)+sin (3φ/2)] for CH,CH₂ and CH₃ moieties respectively. In this expression the θ factorallows for the sensitivity of the ¹³ C detection coil; the θ and φpulses introduce a sin θ and a sin φ factor; the 2θ[±x,±y] and 2φ[±x,±y]pulses introduce sin² θ and sin² φ factors; and the φ/2 pulse adds thef(φ/2) dependence. Because of the sin³ θ and sin³ θ dependences, signalintensity is suppressed for θ or φ pulse angles near 0°, 180°, 360° andso on.

For some applications using separate ¹³ C and ¹ H coils of differentdimensions and/or orientations, these sin³ θ and sin³ φ factors mayproduce sufficient localization of the sample sensitive volumes.However, for simple surface coils, previous studies indicate that thissample localization is unlikely to be good enough. Once again regardingDEPT as being, in part, composed of ¹ H and ¹³ C spin-echo sequences,then by analogy with depth pulses additional sample localization can begenerated by adding further phase-cycled 2θ and 2φ pulses: ##EQU10## Forsequence [D], the extra 2θ[±x] and 2φ[±y] pulses add -cos 2θ and -cos 2φfactors to expression [18]. The extra 2θ[±x,±y] pulse introduces anothersin² θ factor yielding, overall, signal intensity proportional to

    θ cos 2θ sin.sup.5 θ cos 2φ sin.sup.3 φf(φ/2)[19]

The total number of phase combinations and thus the total number oftransients in each cycle is 256.

Expression [19] has been proven with comprehensive experimental supportfor each factor. FIG. 1 shows the -cos 2θ sin⁵ θ dependence of signalintensity expected for a small angle as a function pf incrementing the θpulse length when using the four ¹³ C pulses in sequence [D]. SimilarlyFIG. 2 shows the -cos 2φ sin³ φf(φ/2) dependence expected for a CH₃group when incrementing the length of the ¹ H pulses in sequence [D]. Inthe latter case, because of the relative increase of the dimensions ofthe phantom sample compared to the dimensions of the smaller ¹ H coil,there was considerable variation of the φ pulse angle across the sample,and correspondence between theory and experiment decreases withincreasing ¹ H pulse angles. Nevertheless, the data clearly supports thevalidity of expression [19]. These experiments and the measurementssummarized in Table 1, were carried out using a 1,9 T, 30 cm boremagnet. The experimental points for FIGS. 1 and 2 and 4 were determinedusing a 9 mm diameter, 1,5 mm thick ¹³ CH₃ OH phantom sample coaxialwith, and near the centers of, a 70 mm diameter ¹³ C surface coil and acoaxial, coplanar, 35 mm diameter ¹ H surface coil. The θ=90° pulselength was 20 μsec. The φ=90° pulse length was 10 μsec.

The degree of sample localization that can be achieved using a ¹³ Csurface coil and a coaxial, coplanar ¹ H coil of half the diameter isrepresented in FIG. 3. Because the θ factors are multiplied by the φfactors, signal intensity is restricted to regions where the "θsensitive volume" overlaps the "φ sensitive volume". The "θ sensitivevolume" is defined by 45°<θ<135° and 225°<θ<315° (see FIG. 1). The "φsensitive volume" is defined by 45°<φ<135° (see FIG. 2).

One unwanted region is where φ˜90° and θ˜270°. However, the θ˜270°region can be eliminated by accumulating 256 transients using sequence[D] with θ changed to (2/3)θ, and a second set of 256 transients with θchanged to (4/3)θ, and summing the two sets in a 2:1 ratio respectively.Results using this 512 transient method, listed in Table 1, wereobtained for a ¹³ CH₃ OH phantom positioned at various places in samplespace. These results clearly show that excellent sample localization canbe obtained. Although the total number of transients (512) in thecomplete cycle is large, applications in ¹³ C in-vivo spectroscopy willin general require at least this number of transients for reasonablesignal-to-noise.

Because of the different f(φ/2) factors for CH, CH₂ and CH₃ groups, thespatial dimensions of the "φ sensitive volume" will also be different.However, -cos 2φ sin³ φ f(φ/2) has its first maximum at φ=93.8°, 90° and86.7° for CH, CH₂ and CH₃ respectively, so this small difference willonly marginally change the dimensions of the final localized volume.

At the centre of the final localized volume, by matching pulse lengthsin initial set-up procedures, θ=φ=90°. Thus maximum polarizationtransfer enhancement is achieved, a factor of 4 over the natural ¹³ Cmagnetization at this point. Obviously this enhancement factor decreasesas θ and φ diverge from 90°, but this is the origin of the spatialselectivity.

Other DEPT-related sequences may be applied in the same way withseparate inhomogeneous rf coils. For example inverse DEPT whichgenerates polarization transfer in the reverse direction from ¹³ C to ¹H, may be used by modifying the basic sequence in a very similar way tothe generation of sequences [B] and [D]. Inverse DEPT enables theselective detection of protons attached to ¹³ C nuclei in ¹³ C labelledmetabolites, which has the potential advantage of a very large gain insensitivity over ¹³ C spectroscopy.

Sample localization can be achieved using heteronuclear techniques otherthan DEPT and related polarization transfer methods. These othertechniques rely on a different pulse sequence mechanism but stillutilize the overlap of the two heteronuclear sensitive volumes from theseparate heteronuclear rf transmitter coils. The shape of the sensitivevolume for one of the two heteronuclei is still generated using depthpulse type schemes. However, for the second heteronucleus, the shape ofthe sensitive volume is determined by the probability of flipping thenucleus between its z eigenstates using an rf pulse at a particularpoint in the pulse sequence. If the pulse angle is φ, the probability offlipping is 1/2(1-cos φ), the probability of not flipping is 1/2(1+cosφ), and the difference between the probability of not flipping andflipping is cos φ (Pegg et al, Journal of Magnetic Resonance, 44, 238(1981)). If the pulse applied to the second heteronucleus is a compositepulse, i.e. a sequence of pulses of different phases (Freeman et al,Journal of Magnetic Resonance, 38, 453 (1980)), then probabilities stilldepend on cos φ where φ is the final overall angle through which aninitial z axis vector is rotated by the composite pulse. For an initialz axis vector of unit magnitude, cos φ is the z axis component remainingafter the composite pulse, and this component can be readily calculatedfrom simple three-dimensional geometry. Listing some of the intermediateresults as well, and beginning with a unit z axis vector, we have aftera δ₁ [x] pulse:

    z component=cos δ.sub.1                              [ 20]

    y component=sin δ.sub.1                              [ 21]

    x component=0,                                             [22]

and after a δ₁ [x]; δ₂ [y] composite pulse:

    z component=cos δ.sub.1 cos δ.sub.2            [ 23]

    y component=sin δ.sub.1                              [ 24]

and after a δ₁ [x]; δ₂ [y]; δ₃ [x] composite pulse:

    z component=cos δ.sub.1 cos δ.sub.2 cos δ.sub.3 -sin δ.sub.1 sin δ.sub.3                           [ 25]

Results [20], [23] and [25] are used below to calculate the dependenceof signal intensity on the pulses applied to the second nucleus for twodifferent heteronuclear methods, included here as examples.

EXAMPLE 1 Detection of ¹³ CH_(n) groups in ¹ H NMR using the carbon-flipspin-echo method

Consider the sequence: ##EQU11## The add/substract signifies addition ofthe transients resulting from the first experiment and subtraction oftransients resulting from the alternate second experiment, and thiscancels all ¹ H signals except those arising from ¹³ CH_(n) groups. The¹ H signal arising from ¹³ CH_(n) groups for the first experiment isproportional to cos φ₁, i.e. the probability that the φ₁ pulse does notflip the ¹³ C nuclei between the z eigenstates minus the probabilitythat the pulse does flip the nuclei. Similarly, the alternate experimentyields ¹³ CH_(n) signals proportional to cos φ₂, so overall

    signal intensity ∝1/2(cos φ.sub.1 -cos φ.sub.2)[26]

If φ₂ ≡φ and the φ₁ pulse is omitted, i.e. φ₁ =0 then from [7],

    signal intensity ∝1/2(1-cos φ.sub.2)=sin.sup.2 (φ/2)[27]

Thus a ¹³ C sensitive volume determined by sin² (φ/2) is generated. Thisis probably not restrictive enough for a ¹³ C surface coil, but may besufficient for other rf coil shapes. If the φ₁ pulse is replaced by thecomposite pulse, (φ/2)[x]; φ[y]; (φ/2)[x] and the φ₂ pulse by thecomposite pulse φ[x]; φ[y] then from equations [25] and [23]respectively, equation [26] becomes

    signal intensity ∝1/2(cos.sup.2 (φ/2) cos φ-sin.sup.2 (φ/2)-cos.sup.2 φ)=sin.sup.4 (φ/2)            [28]

The sin⁴ (φ/2) dependence will give a sufficiently restricted sensitivevolume for a ¹³ C surface coil. The experimental data in FIGS. 4(a) and(b) show the expected sin² (φ/2) and sin⁴ (φ/2) dependences of signalintensity obtained by incrementing the φ pulse length of the ¹³ C pulseswhen using sequence [E] and the φ₁ and φ₂ pulses specified above.

To exemplify the use of the method, FIG. 3 is again relevant with thelarge coil being the ¹ H coil and the small coil the ¹³ C coil. The ¹³ Csensitive volume generated by the small coil will depend on sin² (φ/2)or sin⁴ (φ/2) as given by equations [27] or [28]. For an inhomogeneousrf coil such as a surface coil, the π/2 and π¹ H pulses in sequence [E]will be replaced by θ and 2θ[±x,±y] respectively. The ¹ H sensitivevolume can be restricted at will by adding further phase-cycled ¹ Hpulses such as 2θ[±x] or 2θ[±x,±y] in the usual way for depth pulseschemes. Overall, significant signal intensity will only be obtainedfrom the region where the ¹ H sensitive volume overlaps the ¹³ Csensitive volume.

EXAMPLE 2 Detection of ¹³ CH_(n) groups in ¹ H NMR by selectivepolarization transfer

For simplicity we will discuss only the case of a methine group, i.e. ¹³CH, as an example. With some variations, the method will work for themore complicated coupled multiplets of ¹³ CH₂ and ¹³ CH₃ groups and willalso work for polarization transfer in the reverse direction to yieldselective ¹³ C spectra.

For a ¹³ CH group, polarization can be transferred from carbon to protonby inverting one half of the ¹³ C magnetization, i.e. by applying aselective π pulse to one line of the doublet in the ¹³ C spectrum, C_(A)say, and then applying a π/2 proton pulse (Jakobsen et al, Journal ofMagnetic Resonance, 54, 134 (1983)). Alternatively, a selective π pulsecan be applied to the other line of the ¹³ C doublet, C_(B), followed bya (π/2) [H] pulse. The polarization transfer signal may be accumulatedfrom the two experiments by subtracting the result of the second fromthe first, and this alternate addition/subtraction eliminates all other¹ H signals. If the pulse applied to the carbon nuclei is some variableangle φ, as occurs for an inhomogeneous rf coil, the sequence may bewritten: ##EQU12## and it is easily shown that signal intensity isproportional to the probability that the φ pulse flips the carbon nucleifrom the z to the -z eigenstate, i.e. signal intensity ∝1/2(1-cos φ)

Sequence [F] can be extended by applying selective pulses to both C_(A)and C_(B) : ##EQU13## leading to

    signal intensity ∝1/2(1-cos φ.sub.2)-1/2(1-cos φ.sub.1)=1/2(cos φ.sub.1 -cos φ.sub.2),       [29]

i.e. identical with equation [26]. Thus, for example, the φ₁ and φ₂pulses may be chosen as in the above examples which led to equations[27] and [28], and so the ¹³ C sensitive volume may be generated asdescribed for the carbon-flip spin-echo method. If the ¹ H coil is alsoan inhomogeneous radiofrequency coil, the π/2[H] pulse becomes θ anddepth pulse schemes may be added to generate a restrictive ¹ H sensitivevolume again in an analogous fashion to that described in the previousexample. Once more, significant signal intensity will only be obtainedfrom the region where the ¹ H sensitive volume overlaps the ¹³ Csensitive volume.

In the above Examples 1 and 2, only one specific example of compositepulses (which led to equation [28]) was given. There are many otherpossible useful composite pulses. For example, Shaka and Freeman,Journal of Magnetic Resonance, 59, 169 (1984) and Tycko and Pines, 60,156 (1984) have described a family of composite pulses, consisting of 3,9, or 27 single pulses. Any of these may be used for φ₂ with φ₁ =0 ineither of Examples 1 and 2.

                  TABLE 1                                                         ______________________________________                                        Relative signal intensities (%) obtained from a 9 mm                          diameter, 1.5 mm thick, .sup.13 CH.sub.3 OH phantom sample located at         various positions relative to a 70 mm diameter .sup.13 C surface coil         and a coaxial coplanar, 35 mm diameter .sup.1 H surface coil..sup.a           depth (mm) distance along axis 45° to B.sub.o (mm)                     (x axis)   0        10        20    30                                        ______________________________________                                         0         .sup. --.sup.b                                                                         --        --    --                                         5         --       --        --    --                                        10         --       --        --    --                                        15         --       --        18    --                                        20         13       97        56    --                                        25         100      74        10                                              30         24       15        --                                              35         --       --        --                                              ______________________________________                                         .sup.a The phantom was positioned in a plane 45° to B.sub.o, the       main field axis. The plane of the phantom was parallel to the plane of th     coils. The θ and φ pulses were both set at 50 μsec.              .sup.b Signal intensity less than noise level, i.e. <2%.                 

We claim:
 1. A method of operating a nuclear magnetic resonancespectrometer in relation to a sample comprising two types of nuclearmagnetic resonators, by applying to the sample a sequence ofradiofrequency pulses and delay periods, the pulses thereof comprisingradiofrequency bursts of two different radiofrequencies corresponding tothe resonant frequencies of the two types of magnetic resonators, suchthat the scaler coupling interactions between the two types of magneticresonators are allowed to evolve, characterized in thatpulses of rfbursts at one of the two radiofrequencies are applied to one of twospaced coils and pulses of rf bursts at the other radiofrequency areapplied to the other coil, the two spaced coils being shaped andpositioned to provide inhomogeneous rf fields in the sample to overlapsensitive volumes of their rf fields at a region of the sample so thatNMR signal emission of greatest intensity will be obtained from theoverlapping sensitive volumes.
 2. A method as claimed in claim 1 whereinthe radiofrequency pulse sequence used in a DEPT or inverse DEPTsequence, said pulse sequence being modified by inclusion ofphase-cycled radiofrequency pulses, in the manner of depth pulseschemes, for both types of resonators to generate the two overlappingsensitive volumes.
 3. A method as claimed in claim 1 wherein theradiofrequency pulse sequence comprises a spin-echo sequence applied toone type of resonator, said spin-echo sequence being modified byinclusion of phase-cycled radiofrequency pulses, in the manner of adepth pulse scheme, to generate a sensitive volume for the first type ofresonator, and a radiofrequency pulse, or composite radiofrequencypulse, being applied during of the spin-echo delay period to the secondtype of resonator such that a sensitive volume is generated for thesecond type of resonator, the said radiofrequency pulse, or compositeradiofrequency pulse being modified in alternate experiments, thesignals resulting from said alternate experiments being subtracted.
 4. Amethod as claimed in claim 1 wherein the radiofrequency pulse sequenceis a selective polarization transfer sequence wherein the sensitivevolume for the first type of resonator is generated by applying twodifferent selective radiofrequency pulses, or selective compositeradiofrequency pulses, to two lines of the scalar coupled multiplet ofthe first type of resonator, and wherein the sensitive volume for thesecond type of resonator is generated by inclusive of phase-cycledradiofrequency pulses, in the manner of a depth pulse scheme, for thesecond type of resonator.